It is actually a function of SharePoint that it recognises MS-Word as a file format it knows how to embed meta-data in. It does not know how to do this for PDF files.
What you can do (using code or a third party product) is to embed the meta-data in the PDF as a watermark. (Disclaimer, I work for a company that makes such as product)
You can also take it much further and use event receivers or workflows (and a lot of code) to embed the meta data inside the PDF (XMP meta data) whenever the meta data or PDF file is updated. When the file is then uploaded elsewhere you can copy the meta data back.